Newton’s three laws of motion along with his law of gravity is the foundation of classical mechanics. Newton’s first law is know as the law of inertia. We will go into more details later for each of the three laws. The second law can be described by the formula F=ma where F is the Force, m is the mass, and a is the acceleration. This law describes the acceleration of an object with a certain mass when a force acts on it. The third law is know as the action equals reaction law. These three law has tremendous application in our everyday life. If you ever driven a car Newton’s three laws are working under the hood. How about the time your car broke down or ran out of gas and you have to push it along. Well newton’s three laws was there with you. Ever been on a airplane. Well Newton’s law was there to help fly the plane. How about the washing machines that we use to wash our cloths. Well Newton’s law helped built that machine. When engineers was designing the Golden gate bridge, Newton’s laws was there. When Neil Armstrong first set foot on the moon, you got it, Newton’s laws help made it possible. Ever gone bunggy jumping or parachuting well Newton’s laws applies there also. It really amazing how Newton’s laws has so much application in our everyday life. But hold on a minute. What about Einstein’s theories of relativity?

Einstein’s theories of relativity is a improvement on Newton’s three laws of motion and his law of gravity. We could use Einstein’s theories to help built a bridge or calculate the orbit of the space shuttle. But if Newton’s laws is sufficient for the job why spend the energy using a more complex theory. On Earth and

around most of the solar system, the velocities and energies are small enough that Newton’s laws are a good enough approximation to do most jobs. Its only when the velocities approaches the speed of light or when the gravitational force is large does Newton’s laws completely breaks down that we need to switch to Einstein’s laws.

Newton’s first law is also know as the inertial law and is state as an object at rest will stay at rest unless acted upon by a force, an object in motion will stay in motion at a constant velocity (constant velocity means at the same speed and direction) unless acted upon by a force. According to Newton’s first law all object with mass have a property called inertial. One measure of inertial is the mass of the object. If one object has twice the mass as another object. Then the first object has twice the inertial. Simply stated inertial describes the resistance of an object to a change of motion.

Another way to see this is most objects with mass are very lazy. If they are just sitting around they are just too lazy to start moving on their own. They need a force of some kind to start their motion. If they are already in motion they are still too lazy to either speed up, slow down, or change directions. They again required a force. For example, if your car is just sitting around it requires a force (from the engine) to get it going. If your car is already moving at 70 mph it requires a force (a friction force from your brakes, engine, and drivetrain) to slow it down. If you want to make a right turn you need a force (the friction force between your tires and the road) to turn the car.

Have you ever had the unfortunate opportunity to push your car or a shopping cart. A object with a large mass requires more force to change its motion. If an object has twice the mass it also has twice the resistance to a change of motion. Don’t you think is easier to turn an empty shopping cart then the one waiting in the cashier line loaded with goodies.

So, the inertial law tell use that a force is require to change an object’s motion. But how much force is needed? How will it change an object’s motion. That where Newton’s second law comes in.

Newton’s Second Law or sometime known as the F=ma law is truly the workhorse of classical mechanics. When a force F is acting on an object with mass m, the second law describes how it will change the object’s motion. That’s where the a comes in, a stands for acceleration. I’ll give some examples in a moment, but first we must discuss the units used in the second law.

The unit we will be using is known as the MKS units. The M means we will be measuring length in meters. The K means we will be measuring mass in kilograms and S means we will be measuring time in seconds. The unit of force F is the Newton (N for short), named in honor of, you got it, Sir Isaac Newton. As we have said mass m is measured in kilograms (kg). The acceleration a is measured in meters per second per second or m/s/s. So let do some examples, can you say word problems. Actually the following aren’t too bad so follow along.

Example 1:

Example 2:

Example 3:

Example 4:

One word of caution. There might be some misunderstanding here. An object will accelerate as long as a force is action on it. Once the force is remove, there is no more acceleration. Remember a=F/m if F=0, a will also be zero. But this does not mean that the object is not longer moving once the force is removed. Remember Newton’s first law? An object in motion will stay in motion in a constant direction unless acted on by a force.

So you have it, Newton’s second law is actually where the action is, at least in the Math sense. Speaking of action we come to the last of Newton’s three laws, action equals reaction.

Newton’s third is also known as the action equal reaction law. It is stated as for every action there is always an equal and opposite reaction. Note the word opposite. It means that the reaction is always in the opposite direction of the action. Basically this says that forces always comes in pairs. You will never find a single lonely force acting on an object. Both forces in the pair have exactly the same magnitude but act in different directions. Here’s some examples.

We you push on a shopping cart, does it push you back? Of course it does. To understand why this is so, suppose you are in a skating ring and you push against a wall of the ring. What happens? Because of the low friction of the ice, when you push on the wall, you are propel backwards and start moving away from the wall. But remember Newton’s first law or the inertia law? An object at rest stays at rest unless act on by a force. So, in order to move you away from the wall of the skating ring a force must be acting on you. But where is the force coming from? The force that is pushing you away from the wall is actually coming from the wall. Think about it, when you push against the wall, the wall does not move because it is immobile, but you move because the wall pushes back and the ice surface your standing on is of low friction. So there you have it, the action force in this case is you pushing on the wall and the reaction force is the wall pushing on you in the opposite direction.

Hold on a minute, wasn’t there something about an equal but opposite force in Newton’s third law? Well, back to the skating ring again, but this time you brought along your twin brother/sister. Let’s just suppose you have a twin brother or sister and also lets just assume that your twin brother or sister has exactly the same mass as you do. Take your twin and stand face to face in the middle of the skating ring. Now let one of you push, lets say you push on your twin. What happened? You will notice that you will move in one direction and your twin will move in the opposite direction. You will also notice that both of you are moving away with the same speed. This is because when you push on you twin (the action force) your twin pushes on you (the reaction force) with equal magnitude and in the opposite direction. Now according to Newton’s second law F=ma you and your twin’s acceleration will be the same because both of you have identical mass. Remember, a=F/m and m, the mass is the same for both of you, and F is also the same (Newton’s third law, the action force is equal to the reaction force) then the acceleration for you and your twin is also the same. Go it now?

Let revisit the supermarket with the shopping cart. You push on the shopping cart (the action force) and the shopping cart pushes you in the opposite direction with equal magnitude ( the reaction force). But the shopping cart is moving and your not. This is because the shopping cart is on wheels and your not. Try to do the same in the skating ring with a loaded shopping cart.

So there you have it Newton’s three laws of motion. The first law or the law of inertial states that an object at rest will stay at rest unless act on by a force and an object in motion will stay in motion in a constant direction unless acted on by a force. Remember, one measure of inertial is the object’s mass. The more mass an object has the more inertial or resistance to a change in motion the object has. Newton’s second law is describe by the equation F=ma where F is the force action on an object, m is the mass of the object and a is the acceleration the object undergoes. Newton’s third law is stated as for every action there is an equal but opposite reaction. Remember, forces always come in pairs.

Following are some excercises see if you can ace them.

1. If an object has a mass of 10kg and a second object has a mass of 20kg. What can you say about the inertial of the second object compare with the first.

Answer: The second object has twice the inertial and twice the resistance to a change of motion as the first object.

2. A shopping cart has a mass of 50kg, and you push with a force of 10N. What is the acceleration of the shopping cart?

Answer: Using Newton’s second law F=ma divide both sides of the equation by m and your get a=F/m. Using F=10N and m=50kg we have a=F/m=10N/50kg=1/5(m/s/s). Remember 1N/kg=1m/s/s.

3. When you are pulling the rope in a tug of war with the other side of the rope tide to a wall, does the rope pull you back?

Answer: According to Newton’s third law for every action there is an equal and opposite reaction. When you pull on the rope (the action force) the rope pulls back on you (the reaction force) with equal magnitude but in the opposite direction. What happens when your feet looses traction with the ground? You are pull forward by the rope.

4. If an object is accelerating at 10m/s/s due to a force of 100N acting on it, what is the mass of the object? Again using Newton’s second law F=ma. This time we divide both sides of the equation by a, the acceleration and we get m=F/a. Using F=100N and a=10m/s/s, we have m=F/s=100N/10m/s/s=10kg. Remember 1N/1m/s/s = 1kg.
5. Ever seen the pull the table cloth out from the dishes trick? You have a table full of dishes on top of the table cloth. If you pull hard and fast enough you can pull the table cloth out from the dishes without also pulling the dishes off the table. How is this done?

Answer: Newton’s first law applies here. All the dishes on top of the table cloth have inertia or a resistance to a change of motion. When the dishes are at rest on the table cloth they will not want to move. Now if you pull the table cloth fast enough there isn’t enough friction force between the table cloth and the dishes to pull the dishes along.

6. At the skating ring you push on the wall with a force of 100N and you have a mass of 50kg. What will happen?